Answer:
For problem 14, (x = 27). For problem 15, (x = 8)
Explanation:
For problem number 14. You realize this is a septagon with 7 angles.
There is a theorem that says the interior sum of the angles equals 180*(number of angles - 2)
So here Total sum = 180*(7 - 2) = 180 * 5 = 900 degrees
Add the expressions to get an equation in x.
135 + (5x - 4) + (7x -64) + 120 + (6x - 8) + (4x +15) + (3x + 31) = 900
Simplify:
135 - 4 - 64 + 120 - 8 + 15 + 31 + 5x + 7x + 6x + 4x + 3x = 900
301 - 76 + 25x = 900
225 + 25x = 900
25x = 900 - 225
25x = 675
x = 675/25 = 27.
Problem #15.
Find the other angle supplementary to 71 degrees (the exterior angle)
We get: 180 - 71 = 109 degrees
There are four interior angles here.
The interior sum of these angles is 180*(4 - 2) = 180 * 2 = 360 degrees
(10x +6) + 109 + (8x -1) + (13x - 2) = 360
10x + 8x + 13x + 6 + 109 -1 - 2 = 360
31x + 112 = 360
31x = 360 - 112 = 248
x = 248/31 = 8